This invention relates generally to optical systems, such as telescopes, and more specifically to a method and apparatus for estimating the average displacement between surfaces or apertures by generating a two-dimensional power spectrum of a far field fringe pattern that includes extractable information of the average displacement.
Telescopes can provide glimpses at astronomical wonders that dazzle the imagination and can even operate as windows into the past. Electromagnetic radiation collected by telescopes can provide incites into the origin and development of the solar system, the Milky Way, and even the universe. With telescopes astronomers can witness the birth of stars and their fiery deaths. Telescopes have been even been used to estimate physical constants, such as the speed of light, and have been used to prove scientific principles once held in controversy, such as the principles of general and special relativity and the even the existence of black holes. Telescope are being made larger and larger to provide images relatively farther into the past and in relatively greater detail.
As telescopes, and particularly their collecting mirrors, are made relatively larger, maintaining optical integrity has become problematic. For example, as monolithic-telescope mirrors are made relatively larger, gravitational pull, which has relatively little deleterious effect on relatively small mirrors, tends to cause relatively large monolithic mirrors to warp under their own weight. Thermal gradients, which also tend to have relatively little deleterious effect on relatively small mirrors, tend to warp relatively large monolithic mirrors such that resolving power is adversely affected. Monolithic telescope mirrors, such as the matching 8.1 meter mirrors of the Gemini North Telescope on Hawaii's Mauna Kea and the Gemini South Telescope on Chile's Cerro Pachón, continue to be made despite the known troubles with such large mirrors. One solution to reduce warping of such large mirrors is to cut a honeycomb pattern into the backs of the mirrors, thereby reducing weight. Having a reduced weight, gravity tends to adversely affect honeycombed mirrors relatively less than non-honeycombed mirrors. Another technique commonly used to limit telescope mirrors from becoming misshapen, is to refrigerate the mirrors during the day to keep the temperature of the mirrors at their expected nighttime viewing temperature. While refrigeration helps to some extent to reduce temperature gradients in mirrors, mispredicted weather can foil such schemes.
Another technique used to reduce warping of large telescope mirrors is to segment the mirrors into mirror segments that are relatively light and have manageable sizes. Two relatively large telescope mirrors that are formed from mirror segments include the matching 10 meter mirrors of the twin Keck Telescopes on Hawaii's Mauna Kea. Fach Keck Telescope mirror is formed from a mosaic of 36 hexagonal mirror segments arranged in the form of a honeycomb. Each mirror segment is about 1.8 meters wide. Making the large 10 meter mirrors from mirror segments provides a mirror that is relatively light and less susceptible to flexing under its own weight. For example, each 10 meter mirror of the twin Keck Telescopes weighs about the same as the 5 meter monolithic mirror of the Hale Telescope on California's Mount Palomar. While multi-segmented mirrors have solved to some extent the weight and flex problems associated with relatively large monolithic mirrors, other problems arise. For example, the relative piston (or relative height displacement) of segmented mirrors tends to reduce the resolving power of a telescope mirror formed from the segmented mirrors. FIGS. 1A and 1B show top and cross-sectional views of a pair of hexagonal mirrors 10a and 10b having a non-zero relative piston 15. Reducing the relative piston (also commonly referred to as phasing) of the segmented mirrors is often required for causing the mirror segments to function together as a relatively high resolving optic.
Current methods of estimating the relative piston of a pair of surfaces (e.g., mirrors 10a-10b) or discontinuous apertures are both calculation intensive and their accuracy tends to be limited to approximately one wavelength in the visible spectrum. Known methods include, for example, generating a fringe pattern by reflecting a light beam off a pair of mirrors and passing the reflected light through a dispersed fringe sensor (DSP). DSPs tend to disperse the reflected light and generate a fringe pattern, which includes relative piston information of the pair of mirrors. The relative piston information is extracted from the fringe pattern by fitting line slices of the fringe pattern to a sinusoidally varying function, such as a cosine function. However, as fringe patterns generated from DSP methods do not precisely fit to a sinusoid, such methods of estimating relative piston have limited accuracy. While accuracy can be improved by further calculations, such calculations add significantly to the computing power required to improve relative piston estimates, thus driving up the costs of such schemes.
Accordingly, new methods and systems are desired for estimating the relative piston of segments (such as telescope mirror segments) and discontinuous apertures that are relatively less calculation intensive and generate relative piston data in, for example, the nanometer range. Methods and systems that can generate relative piston data in the nanometer range can in turn be used to reduce the relative piston to approximately the same range, thus improving the resolving power of optical systems having segmented optics.